Seven original elements

Neodymium was discovered in 1885 by Austrian chemist Carl Auer (Baron von Welsbach 1858—1929). Auer found the new element in a mineral called didymia. Didymia, in turn, had been found in another complicated mineral known as ceria, originally found in Sweden in 1803. It took chemists nearly a century to completely analyze ceria. When they had done so, they found that it contained seven new elements. Neodymium was one of these elements. 

The methyl radical, CH3, with a planar trigonal structure, looks the same if it is rotated by 120, 240, or 360° about an axis (C3 axis in Fig. 5.18) perpendicular to the plane containing three equivalent carbon atoms. An operation that leaves a molecule (object) looking the same (or sending into itself or a position indistinguishable from the original) is a symmetry operation. Symmetry operations include seven symmetry elements in Table 5.6 which are commonly possessed by molecular systems. 

The Marshall Unker [23] has been widely used to synthesize compounds that can be cleaved by primary and secondary amines to afford the corresponding amides. Marshall linker was used in the synthesis of three or more diversity-site hbraries because it allowed the addition of one more diversity element at the cleavage step. While the original reported linker [23] involved the oxidation of the Unker before cleavage, the efficient release of the resin-bound compounds using nucleophiles from the unoxidized linker has been reported [16, 24]. Similarly to the acid-labile linkers, the kinetics of the cleavage reaction and time required for this reaction directly affect the synthesis efficiency, purity and yield of the final products. A cleavage study was carried out on seven resin-bound thiophenol esters (34—40) on Marshall Unker with 3 amines (41-43) (Scheme 12.11 and Tab. 12.4). 

Kelly and coworkers concluded that a combination of only seven (of the 50) elements measured, and the isotopic ratios of C and O, gave 100 percent discrimination between rice samples from any of the three continental land masses, and that measurement of just B and Mg was sufficient to allow a reasonable indication to be gained as to whether the rice had originated in the United States. This statement underlines the comment made in an earlier section of the chapter, regarding the importance of establishing the question-to-be-asked, or the answer-that-is-required, when designing an authenticity study. 

In cesium chloride the main contribution to V2 comes from cesium ion states acting as intermediaries in a form that can be obtained from perturbation theory. We need not be further concerned here with the origin of Fj. (We shall discuss the ionic crystal matrix elements in Chapter 14.) For a particular value of J in Eq. (2-2), there are only seven values of i that contribute to the sum / = j numbered as 0, and the six nearest-neighbor chlorine s states. The solution (valid for any j) is... 

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